MAA509: Quantum Computing and Information Introduction

Transcription

1 MAA509: Quantum Computing and Information Introduction November 7, 2016 November 7, / 19

2 Why make computers? Computation by hand is difficult and not very stimulating. Why not make a machine do it for you? It was 1949 in Southern California. Our computer was a very new CPC (model 1, number 1) a 1 - second - per - arithmetic - operation clunker that [...] represented a tremendous, if as yet unrealized, increase in computing capacity over a roomful of girls with desk calculators. Forman S. Acton Numerical Methods That (Usually) Work November 7, / 19

3 Early computers were specialized Machine designed to aid a specific task, mechanical version of a modern program. November 7, / 19

4 Later computers less specialized Machine that could be programmed and solve several different problems. November 7, / 19

5 Some important names Charles Babbage Alan Turing John von Neumann Konrad Zuse Richard Feynman David Deutsch Peter Shor November 7, / 19

6 Charles Babbage ( ) Designed some of the very first general-purpose mechanical computers. The Difference Engine and the Analytical Engine. Neither were finished during his lifetime but both worked (with minor adjustments). November 7, / 19

7 Alan Turing ( ) Formulated the very first general-purpose theoretical computer. The Turing Machine is an abstraction of a computer program, the Universal Turing Machine is an abstraction of a programmable computer. Also famous for cracking the German Enigma encryption machine. November 7, / 19

8 John von Neumann ( ) Significant contributions to many major branches of mathematics and physics, computer science and economics. Created the von Neumann architecture which is the basic architecture for almost all modern computers, also worked on the ENIAC. Also famous for working on the Manhattan project and an important figure in the formulation of quantum mechanics, game theory and set theory among other things. November 7, / 19

9 Konrad Zuse ( ) Constructed the very first fully programmable computer, the Z3 in Worked almost completely isolated from other computer scientists, did not even consider Turing-completeness (but achieved it anyway). November 7, / 19

10 Richard Feynman ( ) Well-known and successful theoretical physicist, also worked on the Manhattan project, received the Nobel Prize for his work on quantum physics in One of the first (shortly after and independent of Yuri Manin) to describe how quantum computation might be faster than classical computation. Suggested that quantum computers can simulate multi-particle quantum systems efficiently. November 7, / 19

11 David Deutsch (1953 -) British physicist working at the University of Oxford. First to describe the Universal Quantum Turing Machine in Numerous other contributions to the field, for example the Deutsch-Jozsa algorithm. November 7, / 19

12 Peter Shor (1959 -) American professor of applied mathematics working at the Massachusetts Institute of Technology. Constructed two of the most famous algorithm in quantum computation, Shor s algorithm (for factorizing integers into prime factors) and Shor s code (for error-detection and error-correction on qubits). November 7, / 19

13 What is classical computing? (simplified) 0 or 1 Classical computing is performed by manipulating bits (binary values). Two possible operations: flip the bit, or leave it unchanged. Still quite useful. November 7, / 19

14 What is quantum computing? (simplified) 0 ψ ψ = a 0 + b 1, a, b C ϕ θ 1 Quantum computing is performed by manipulating qubits (complex valued vectors in a Hilbert space). Infinitely many possible operations: rotations on the Bloch sphere. Can do certain things much faster than a classical computer (for instance factoring integers into prime factors). November 7, / 19

15 Why is quantum computing powerful? Main reason that quantum computing is more powerful than classical computing is quantum parallelism: under certain circumstances a quantum computer evaluate all possible solutions at once. Quantum phenomena is often a problem for classical computational technology when it is shrunk small enough, so exploiting them to increase performance is very desirable. Quantum computers can simulate quantum-mechanical systems more efficiently than classical computers. November 7, / 19

16 Do we have quantum computers? Experimental with few qubits (below 10 for solid state, more for optical). Impractical, very large and operate only at specific temperatures. Maybe the D-Wave is a (specialised) quantum computer, but the jury is still out. Most agree that quantum computers will be (relatively) common in a matter of decades. November 7, / 19

17 Why study this course? Interested in computer science, even if it is not practically useful yet. Very useful practice in learning to use and interpret complex and specialized mathematical language and gives insight into some very general problems and applications of abstract mathematics without having to learn a lot of computer science and physics. November 7, / 19

18 Important questions in computer science and information theory Can a problem be solved? How fast can a problem be solved? How reliably can a problem be solved? How can I describe information efficiently? How can I describe information reliably? How can I send information efficiently? How can I send information reliably? How can I send information safely? November 7, / 19

19 How will this course work? Lectures on various topics related to quantum computing and information: Basic quantum computing: Qubits and quantum gates Qubit registers and quantum circuit Computability, (time) complexity, algorithms Quantum algorithms Will be primarily tested in the seminar assignments. Classical and quantum information and computer science related topics: Quantum algorithms Classical and quantum information theory Classical and quantum cryptography Will be primarily tested in the projects. Final grade determined by a weighted average of grades for the seminar assignments and the project, see the study guide for details. November 7, / 19